Motor spindle control system and method

ABSTRACT

A control system and method for a multi-phase motor substantially reduces or eliminates jitter resulting from drive mismatch by replacing a conventional trapezoidal drive profile with a drive profile that causes the voltage applied across active phases of the motor to match the back-EMF across those phases. In an ideal motor, the back-EMF is substantially sinusoidal, and although the drive profile applied to each phase is not truly substantially sinusoidal, the drive voltage across the active phases is substantially sinusoidal. In a non-ideal motor, the back-EMF is not truly sinusoidal and the drive profiles applied to each phase are calculated to cause the drive voltage across the active phases to match the back-EMF across those phases.

CROSS REFERENCE TO RELATED APPLICATION

This claims the benefit of copending U.S. Provisional Patent ApplicationNo. 60/823,306, filed Aug. 23, 2006, which is hereby incorporated byreference herein in its entirety.

BACKGROUND OF THE INVENTION

This invention relates to a system and method for controlling thespindle of an electric motor, and more particularly to a system andmethod for controlling the spindle of a motor that rotates the platterof a disk drive.

Controlling the speed at which the platter of a disk drive rotates isvery important, particularly as storage densities increase and plattersize decreases. Thus, in a microdrive—i.e., a drive having a platterdiameter of about 1 inch or less—even a small error in angular positionmay result in an incorrect sector being read or written.

One source of error in angular position is jitter resulting fromirregularities in motor speed. One source of jitter is a mismatchbetween the motor drive profile, which is the voltage pattern applied todrive the motor, and the motor itself. One common type of motor used ina disk drive is a three-phase motor having four or six poles, whichideally has a sinusoidal drive profile. Such a motor commonly is drivenwith a drive profile that is known as a “trapezoidal” profile, whichapproximates a sinusoidal profile. However, because it only approximatesa sinusoidal profile, a trapezoidal drive profile can result in motorspeed irregularities—i.e., jitter or “torque ripple.” Moreover, atrapezoidal drive profile cannot take into account variations of a motorfrom an ideal motor.

It therefore would be desirable to be able to provide a motor driveprofile that minimizes jitter.

SUMMARY OF THE INVENTION

In accordance with the invention, a drive profile is applied to athree-phase motor, which drive profile results, in the case of an idealmotor, in a true sinusoidal drive current. Moreover, for a non-idealmotor, the drive profile can be adjusted to match the non-ideality ofthe motor.

The drive profile, which is a voltage profile, preferably is applied asdiscrete samples—i.e., it is applied as a number of voltagesamples—e.g., 48 or 96 samples—over a single electrical cycle. While thevoltage profile applied to any one phase of an ideal motor appears closeto sinusoidal, it may not appear truly sinusoidal. However, the voltagedifference between the active phases preferably is substantially trulysinusoidal. Specifically, at any given moment in an ideal three-phasemotor, two phases may be active while one is tristated. In accordancewith the present invention, the difference between the voltage appliedto one phase and the voltage applied to another phase—i.e., the voltagebeing applied across the motor—plotted over time, is substantially trulysinusoidal for an ideal motor.

During motor operation, as each rotor pole passes a stator pole, thepole-pair interaction generates a back-electromotive force, or“back-EMF,” that can be measured. In an ideal motor, the back-EMFprofile across the pair of active phases is substantially trulysinusoidal. However, most motors are not ideal, as a result ofmechanical differences in, inter alia, motor fabrication and coilwindings, so that the back-EMF profile is not sinusoidal. Duringoperation of a non-ideal motor, the back-EMF can be measured andplotted. In accordance with the present invention, the drive profilescan be adjusted to substantially match the measured back-EMF profile,resulting in substantial reduction or elimination of torque ripple orjitter resulting from drive mismatch.

Therefore, in accordance with the present invention, there is provided amethod for controlling a multi-phase motor. The method includesdetecting back-EMF from pole-pair interactions during operation of themotor, deriving, from the detected back-EMF, a back-EMF profile for eachphase pair of the motor, and applying to each phase of the motor atime-varying voltage profile such that time-varying voltage across eachphase pair substantially matches the back-EMF profile for that phasepair.

Motor control apparatus for carrying out the method is also provided.

BRIEF DESCRIPTION OF THE DRAWINGS

The above and other advantages of the invention will be apparent uponconsideration of the following detailed description, taken inconjunction with the accompanying drawings, in which like referencecharacters refer to like parts throughout, and in which:

FIG. 1 is a schematic view of a three-phase motor;

FIG. 2 is a graphical representation of trapezoidal drive profiles for athree-phase motor;

FIG. 3 is a graphical representation of a preferred embodiment of motordrive profiles for an ideal three-phase motor current in accordance withthe present invention;

FIG. 4 is a graphical representation of the phase-to-phase voltages forthe drive profiles of FIG. 3;

FIG. 5 is a graphical representation of a preferred embodiment of motordrive profiles for a non-ideal three-phase motor in accordance with thepresent invention;

FIG. 6 is a graphical representation of the phase-to-phase voltages forthe drive profiles of FIG. 5;

FIG. 7 is a schematic diagram of motor drive circuitry in accordancewith an embodiment of the present invention;

FIG. 8 is a block diagram of an exemplary hard disk drive that canemploy the disclosed technology;

FIG. 9 is a block diagram of an exemplary digital versatile disc thatcan employ the disclosed technology;

FIG. 10 is a block diagram of an exemplary high definition televisionthat can employ the disclosed technology;

FIG. 11 is a block diagram of an exemplary vehicle that can employ thedisclosed technology;

FIG. 12 is a block diagram of an exemplary cellular telephone that canemploy the disclosed technology;

FIG. 13 is a block diagram of an exemplary set top box that can employthe disclosed technology; and

FIG. 14 is a block diagram of an exemplary media player that can employthe disclosed technology.

DETAILED DESCRIPTION OF THE INVENTION

The invention will now be described with reference to FIGS. 1-15.

FIG. 1 shows, schematically, the three phases A (11), B (12) and C (13)of a three-phase motor 10 with which the present invention may be used.It should be remembered that the view of FIG. 1 is theoretical,notwithstanding that it looks like the rotor of a three pole-pair motor.The number of pole-pairs in the motor is completely independent of thenumber of power supply phases and the present invention will work withsubstantially any three-phase motor regardless of the number ofpole-pairs.

As seen in FIG. 1, each phase A (11), B (12), C (13) of motor 10 may bemodeled as a motor resistance R_(motor) 14, a motor inductance L_(motor)15 and back-EMF voltage V_(BEMF) 16 in series between a respective powersupply phase SPA (110), SPB (120), SPC (130) and a central tap C_(tap)17 to which all phases are connected. Although the order of thesecomponents 14, 15, 16 is reversed in phase C (13) as compared to phasesA (11) and B (12), the result would be the same if phase C (13) wereidentical to phases A (11) and B (12).

If phase A (11) is driven high while phase B (12) is driven low, whichmay be referred to as A-nB, current will flow in accordance with arrow111, while if phase B (12) is driven high while phase A (11) is drivenlow, which may be referred to as B-nA, current will flow in accordancewith arrow 112. Similarly, the B-nC condition is represented by arrow121 while the C-nB condition is represented by arrow 122, and the C-nAcondition is represented by arrow 131 while the A-nC condition isrepresented by arrow 132.

The motor power supply can be driven in a known trapezoidal pattern byselecting one phase and driving it high for two pole periods (where eachpole period for an n-pole motor is one nth of one electrical cycle)while alternating which of the other two phases is driven low. Afterthose two periods, the phase that is low is kept low for another phase,while the high phase is switched. This continues until the startingpoint is reached, and then the pattern repeats. Thus for a six-polemotor, selecting phase B (12) as the initial high phase and phase C (13)as the initial low phase, the trapezoidal drive pattern may be B-nC,B-nA, C-nA, C-nB, A-nB, A-nC, and then returning to B-nC. This isillustrated in FIG. 2, where each period I, II, III, IV, V, VI, spans60° of the 360° electrical cycle. When a phase is neither high or low,preferably it is tristated. It will be appreciated that B-nC is notrequired to be the starting point, but is only an example. (In FIGS. 1and 2, each of the low states nA, nB and nC is represented not as nA, nBor nC, but as A, B or C with a horizontal bar above it, referred to as“A-bar”, “B-bar” and “C-bar”).

FIG. 3 shows a preferred embodiment of drive profiles 31, 32, 33 inaccordance with the present invention applied to phases A, B and C,respectively, of an ideal three-phase motor. Each drive profile 31, 32,33 represents voltage applied to a respective phase. As shown in FIG. 3,each profile 31, 32, 33 is applied as a series of discrete samples. Inthis preferred embodiment, 96 samples are applied during each completeelectrical cycle, but another number—e.g., 48 samples—may be applied.Alternatively, each drive profile could be applied as a continuousanalog signal, but when using digital (e.g., microprocessor-based)control circuitry, applying the profile as discrete samples is easier.Preferably, the number of samples used should be sufficient toapproximate a smooth continuous signal.

Although the drive profiles of FIG. 3 are substantially continuous ascompared to the discrete voltage levels of the trapezoidal driveprofiles of FIG. 2, and although the profiles of FIG. 3 are not shown asstarting in the B-nC state, it can be seen that the drive profiles ofFIG. 3 can be mapped onto the B-nC, B-nA, C-nA, C-nB, A-nB, A-nC patternof periods I-VI of FIG. 2, except that period I starts at 150° insteadof at 0°, and period IV is split between the first and last 30° of the360° cycle.

The drive profiles of FIG. 3 resemble sinusoidal profiles, but are nottruly sinusoidal. For example, each profile is flat or truncated at itsmaxima and minima, representing a “clipped” sinusoid. However, the shapeof the drive profile, representing voltage applied to each phase betweenthe respective coil terminal and central tap C_(tap) 17, is notdeterminative of the drive current. The drive current is determined bythe phase-to-phase voltage for the two active phases in each of periodsI-VI. As seen in FIG. 4, the phase-to-phase voltage profiles 41, 42, 43,derived by plotting the differences between corresponding samples of thetwo active phases in FIG. 3, are substantially truly sinusoidal. Thisresults in substantially sinusoidal drive current in each phase.

FIG. 5 shows drive profiles 51, 52, 53 for an exemplary non-ideal motor.Drive profiles 51, 52, 53 preferably are determined by measuring theback-EMF across the active phase pairs of the non-ideal motor duringoperation and applying drive profiles 51, 52, 53, which are calculatedto result in phase-to-phase voltage profiles 61, 62, 63 of FIG. 6 thatmatch the measured nonsinusoidal back-EMF profiles of the non-idealmotor. It has been determined as part of the present invention thatapplying phase-to-phase voltage profiles that match the back-EMFprofiles of a motor results in a substantially reduction or eliminationof torque ripple or jitter resulting from drive mismatch, although othersources of jitter may remain in the system such as, e.g., pole mismatch,or jitter introduced by the external speed control loops.

FIG. 7 shows an embodiment of control circuitry 70 for practicing theinvention. Control circuitry 70 includes a motor controller 71, a motorcontrol interface 72, and a power supply 73 that provides the threevoltage phases 730, 731, 732 to motor 10. Motor controller 71 issometimes referred to as a Pcombo or power combo chip, and is normallymounted at or near spindle motor 10, controlling both spindle motor 10and the voice-coil motor (not shown) that moves the read/write head.Motor control interface 72 is sometimes referred to as the devicesystem-on-a-chip or “SoC,” and is normally removed from motor 10 itself,as it is the main controller and interface of the device (e.g., a diskdrive) of which motor 20 is a part. The present invention preferably iscarried out in motor control interface 72 by processor 74 thereof, usingmemory 75 thereof.

Preferably, controller 71 includes back-EMF detection circuitry 76 whichpreferably detects the back-EMF profiles across the various phase pairsduring motor operation and preferably stores them in memory 77 orregisters 78. Processor 74 of motor control interface 72 then uses thosestored profiles from memory 77 or registers 78 to compute drive profiles730, 731, 732 for each phase, such that application of those profiles730, 731, 732 to the three phases 11, 12, 13 causes the drive voltageacross active pairs of phases 11-12, 11-13 or 12-13 to match the storedback-EMF profiles.

Thus it is seen that a method and apparatus for controlling a motor byproviding drive voltage profiles that match the motor's back-EMFprofiles, thereby resulting in substantial elimination or reduction oftorque ripple or jitter resulting from drive mismatch, has beenprovided.

Referring now to FIGS. 8 and 9, two exemplary implementations of thepresent invention are shown.

Referring now to FIG. 8 the present invention can be implemented in ahard disk drive 600. The present invention may implement either or bothsignal processing and/or control circuits, which are generallyidentified in FIG. 8 at 602. In some implementations, the signalprocessing and/or control circuit 602 and/or other circuits (not shown)in the HDD 600 may process data, perform coding and/or encryption,perform calculations, and/or format data that is output to and/orreceived from a magnetic storage medium 606.

The HDD 600 may communicate with a host device (not shown) such as acomputer, mobile computing devices such as personal digital assistants,cellular telephones, media or MP3 players and the like, and/or otherdevices, via one or more wired or wireless communication links 608. TheHDD 600 may be connected to memory 609 such as random access memory(RAM), low latency nonvolatile memory such as flash memory, read onlymemory (ROM) and/or other suitable electronic data storage.

Referring now to FIG. 9 the present invention can be implemented in adigital versatile disk (DVD) drive 700. The present invention mayimplement either or both signal processing and/or control circuits,which are generally identified in FIG. 7 at 702, and/or mass datastorage of the DVD drive 700. The signal processing and/or controlcircuit 702 and/or other circuits (not shown) in the DVD drive 700 mayprocess data, perform coding and/or encryption, perform calculations,and/or format data that is read from and/or data written to an opticalstorage medium 706. In some implementations, the signal processingand/or control circuit 702 and/or other circuits (not shown) in the DVDdrive 700 can also perform other functions such as encoding and/ordecoding and/or any other signal processing functions associated with aDVD drive.

DVD drive 700 may communicate with an output device (not shown) such asa computer, television or other device, via one or more wired orwireless communication links 707. The DVD drive 700 may communicate withmass data storage 708 that stores data in a nonvolatile manner. The massdata storage 708 may include a hard disk drive (HDD). The HDD may havethe configuration shown in FIG. 8. The HDD may be a mini-HDD thatincludes one or more platters having a diameter that is smaller thanapproximately 1.8″. The DVD drive 700 may be connected to memory 709such as RAM, ROM, low-latency nonvolatile memory such as flash memory,and/or other suitable electronic data storage.

Referring now to FIG. 10, the present invention can be implemented in ahigh definition television (HDTV) 800. The present invention mayimplement either or both signal processing and/or control circuits,which are generally identified in FIG. 10 at 822, a WLAN interfaceand/or mass data storage of the HDTV 800. The HDTV 800 receives HDTVinput signals in either a wired or wireless format and generates HDTVoutput signals for a display 826. In some implementations, signalprocessing circuit and/or control circuit 822 and/or other circuits (notshown) of the HDTV 800 may process data, perform coding and/orencryption, perform calculations, format data and/or perform any othertype of HDTV processing that may be required.

The HDTV 800 may communicate with mass data storage 827 that stores datain a nonvolatile manner such as optical and/or magnetic storage devices.At least one HDD may have the configuration shown in FIG. 8 and/or atleast one DVD drive may have the configuration shown in FIG. 9. The HDDmay be a mini-HDD that includes one or more platters having a diameterthat is smaller than approximately 1.8″. The

HDTV 800 may be connected to memory 828 such as RAM, ROM, low-latencynonvolatile memory such as flash memory, and/or other suitableelectronic data storage. The HDTV 800 also may support connections witha WLAN via a WLAN network interface 829.

Referring now to FIG. 11, the present invention implements a controlsystem of a vehicle 900, a WLAN interface and/or mass data storage ofthe vehicle control system. In some implementations, the presentinvention may implement a powertrain control system 932 that receivesinputs from one or more sensors such as temperature sensors, pressuresensors, rotational sensors, airflow sensors and/or any other suitablesensors and/or that generates one or more output control signals such asengine operating parameters, transmission operating parameters, and/orother control signals.

The present invention may also be implemented in other control systems940 of the vehicle 900. The control system 940 may likewise receivesignals from input sensors 942 and/or output control signals to one ormore output devices 944. In some implementations, the control system 940may be part of an anti-lock braking system (ABS), a navigation system, atelematics system, a vehicle telematics system, a lane departure system,an adaptive cruise control system, a vehicle entertainment system suchas a stereo, DVD, compact disc and the like. Still other implementationsare contemplated.

The powertrain control system 932 may communicate with mass data storage946 that stores data in a nonvolatile manner. The mass data storage 946may include optical and/or magnetic storage devices for example harddisk drives HDD and/or DVDs. At least one HDD may have the configurationshown in FIG. 8 and/or at least one DVD drive may have the configurationshown in FIG. 9. The HDD may be a mini-HDD that includes one or moreplatters having a diameter that is smaller than approximately 1.8″. Thepowertrain control system 932 may be connected to memory 947 such asRAM, ROM, low latency nonvolatile memory such as flash memory, and/orother suitable electronic data storage. The powertrain control system932 also may support connections with a WLAN via a WLAN networkinterface 948. The control system 940 may also include mass datastorage, memory and/or a WLAN interface (none shown).

Referring now to FIG. 12, the present invention can be implemented in acellular telephone 1000 that may include a cellular antenna 1051. Thepresent invention may implement either or both signal processing and/orcontrol circuits, which are generally identified in FIG. 12 at 1052, aWLAN interface and/or mass data storage of the cellular phone 1000. Insome implementations, the cellular telephone 1000 includes a microphone1056, an audio output 1058 such as a speaker and/or audio output jack, adisplay 1060 and/or an input device 1062 such as a keypad, pointingdevice, voice actuation and/or other input device. The signal processingand/or control circuits 1052 and/or other circuits (not shown) in thecellular telephone 1000 may process data, perform coding and/orencryption, perform calculations, format data and/or perform othercellular telephone functions.

The cellular telephone 1000 may communicate with mass data storage 1064that stores data in a nonvolatile manner such as optical and/or magneticstorage devices—for example hard disk drives (HDDs) and/or DVDs. Atleast one HDD may have the configuration shown in FIG. 8 and/or at leastone

DVD drive may have the configuration shown in FIG. 9. The HDD may be amini-HDD that includes one or more platters having a diameter that issmaller than approximately 1.8″. The cellular telephone 1000 may beconnected to memory 1066 such as RAM, ROM, low-latency nonvolatilememory such as flash memory, and/or other suitable electronic datastorage. The cellular telephone 1000 also may support connections with aWLAN via a WLAN network interface 1068.

Referring now to FIG. 13, the present invention can be implemented in aset top box 1100. The present invention may implement either or bothsignal processing and/or control circuits, which are generallyidentified in FIG. 13 at 1184, a WLAN interface and/or mass data storageof the set top box 1100. Set top box 1100 receives signals from a source1182 such as a broadband source and outputs standard and/or highdefinition audio/video signals suitable for a display 1188 such as atelevision and/or monitor and/or other video and/or audio outputdevices. The signal processing and/or control circuits 1184 and/or othercircuits (not shown) of the set top box 1100 may process data, performcoding and/or encryption, perform calculations, format data and/orperform any other set top box function.

Set top box 1100 may communicate with mass data storage 1190 that storesdata in a nonvolatile manner. The mass data storage 1190 may includeoptical and/or magnetic storage devices for example hard disk drives HDDand/or DVDs. At least one HDD may have the configuration shown in FIG. 8and/or at least one DVD drive may have the configuration shown in FIG.9. The HDD may be a mini-HDD that includes one or more platters having adiameter that is smaller than approximately 1.8″. Set top box 1100 maybe connected to memory 1194 such as RAM, ROM, low-latency nonvolatilememory such as flash memory, and/or other suitable electronic datastorage. Set top box 1100 also may support connections with a WLAN via aWLAN network interface 1196.

Referring now to FIG. 14, the present invention can be implemented in amedia player 1200. The present invention may implement either or bothsignal processing and/or control circuits, which are generallyidentified in FIG. 14 at 1204, a WLAN interface and/or mass data storageof the media player 1200. In some implementations, the media player 1200includes a display 1207 and/or a user input 1208 such as a keypad,touchpad and the like. In some implementations, the media player 1200may employ a graphical user interface (GUI) that typically employsmenus, drop down menus, icons and/or a point-and-click interface via thedisplay 1207 and/or user input 1208. Media player 1200 further includesan audio output 1209 such as a speaker and/or audio output jack. Thesignal processing and/or control circuits 1204 and/or other circuits(not shown) of media player 1200 may process data, perform coding and/orencryption, perform calculations, format data and/or perform any othermedia player function.

Media player 1200 may communicate with mass data storage 1210 thatstores data such as compressed audio and/or video content in anonvolatile manner. In some implementations, the compressed audio filesinclude files that are compliant with MP3 format or other suitablecompressed audio and/or video formats. The mass data storage may includeoptical and/or magnetic storage devices for example hard disk drives HDDand/or DVDs. At least one HDD may have the configuration shown in FIG. 8and/or at least one DVD drive may have the configuration shown in FIG.9. The HDD may be a mini-HDD that includes one or more platters having adiameter that is smaller than approximately 1.8″. Media player 1200 maybe connected to memory 1214 such as RAM, ROM, low-latency nonvolatilememory such as flash memory, and/or other suitable electronic datastorage. Media player 1200 also may support connections with a WLAN viaa WLAN network interface 1216. Still other implementations in additionto those described above are contemplated.

It will be understood that the foregoing is only illustrative of theprinciples of the invention, and that the invention can be practiced byother than the described embodiments, which are presented for purposesof illustration and not of limitation, and the present invention islimited only by the claims which follow.

What is claimed is:
 1. A method for controlling a multi-phase motor,said method comprising: detecting back-EMF from pole-pair interactionsduring operation of said motor; deriving from said detected back-EMF aback-EMF profile for each pair of phases of said motor, by determiningdifferences between back-EMF detected for respective phases in each saidpair of phases; and applying to each phase of said motor a time-varyingvoltage profile such that a time-varying voltage difference between saidphases in each said pair of phases substantially matches said back-EMFprofile for said pair of phases.
 2. The method of claim 1 wherein: saidmotor is a substantially ideal motor; said back-EMF profile for eachsaid pair of phases of said motor is substantially sinusoidal; and saidtime-varying voltage difference between said phases in each said pair ofphases is substantially sinusoidal.
 3. Apparatus for controlling amulti-phase motor, said apparatus comprising: means for detectingback-EMF from pole-pair interactions during operation of said motor;means for deriving from said detected back-EMF a back-EMF profile foreach pair of phases of said motor, by determining differences betweenback-EMF detected for respective phases in each said pair of phases; andmeans for applying to each phase of said motor a time-varying voltageprofile such that a time-varying voltage difference between said phasesin each said pair of phases substantially matches said back-EMF profilefor said pair of phases.
 4. The apparatus of claim 3 wherein: said motoris a substantially ideal motor; said back-EMF profile for each said pairof phases of said motor is substantially sinusoidal; and saidtime-varying voltage difference between said phases in each said pair ofphases is substantially sinusoidal.
 5. Apparatus for controlling amulti-phase motor, said apparatus comprising: a power supply; a motorcontroller including detector circuitry that detects back-EMF frompole-pair interactions during operation of said motor; storageassociated with said motor controller that stores back-EMF measurementsfor each phase of said motor; a motor control interface including aprocessor that reads said stored back-EMF measurements for each phase ofsaid motor to derive a back-EMF profile for each active pair of phasesof said motor by determining differences between back-EMF detected forrespective phases in each said active pair of phases, and derives adrive voltage profile to be applied to each phase of said motor andcommands said motor controller to instruct said power supply to applyeach said derived drive voltage profile to each respective phase of saidmotor, such that a time-varying voltage difference between said phasesin each said pair of phases substantially matches said back-EMF profilefor said pair of phases.
 6. The apparatus of claim 5 wherein: said motoris a substantially ideal motor; said back-EMF profile for each said pairof phases of said motor is substantially sinusoidal; and saidtime-varying voltage difference between said phases in each said pair ofphases is substantially sinusoidal.
 7. Apparatus for controlling amulti-phase motor, said apparatus comprising: power supply means; motorcontroller means including detector means for detecting back-EMF frompole-pair interactions during operation of said motor; storage meansassociated with said motor controller means, for storing back-EMFmeasurements for each phase of said motor; motor control interface meansincluding processor means for reading said stored back-EMF measurementsfor each phase of said motor for deriving a back-EMF profile for eachactive pair of phases of said motor, and for deriving a drive voltageprofile to be applied to each phase of said motor, and for commandingsaid motor controller means to instruct said power supply means to applyeach said derived drive voltage profile to each respective phase of saidmotor, such that a time-varying voltage difference between said phasesin each said pair of phases substantially matches said back-EMF profilefor said pair of phases.
 8. The apparatus of claim 7 wherein: said motoris a substantially ideal motor; said back-EMF profile for each pair ofphases of said motor is substantially sinusoidal; and said time-varyingvoltage difference between said phases in each said pair of phases issubstantially sinusoidal.